1331.0 - Statistics - A Powerful Edge!, 1996

ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 31/07/1998

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Contents >> Stats Maths >> Displaying Information - Graph Types

DISPLAYING INFORMATION: GRAPH TYPES

Information that is presented in a graph can be quick and easy to understand. So it is not surprising that the use of graphs has increased in recent years, particularly in the media (newspapers and television). There are times when information is better presented by graph than by table. This is often the case when there is a trend or comparison to be shown. A graph can do this very effectively.

USING GRAPHS

Knowing how to convey information by graph is important in the presentation of statistics. The following is a list of some general rules to keep in mind when preparing graphs. A graph should:

be simple and not too cluttered,
show data without changing the data’s message,
clearly show any trend or differences in the data, and
be accurate in a visual sense (if one chart value is 15 and another 30, then 30 should appear to be twice the size of 15).

It is also important to know what type of graph to use when presenting statistics. There are several types of graph you can use, which are outlined in the following pages.

BAR GRAPH

A bar graph may be either horizontal or vertical. To differentiate between the two, a vertical bar graph is called a column graph. An important point about bar graphs is the length of the bars: the greater the length, the greater the value.

COLUMN GRAPH

Column graphs are good for comparing values. One disadvantage of column graphs is lack of room for a written label at the foot of each bar; so it is best to use a column graph when the label is short, as in the example below.

PERCENTAGE OF SAME SEX AND AGE GROUP EMPLOYED,
AUSTRALIA, 1996 CENSUS

Graph: percentage of same sex and age group employed during 1996 Census

Notice how a column graph allows you to show more than one series of data in the graph: in the above example, data for males and females.

A careful examination of the column graph on the previous page should allow you to make some basic conclusions about the information shown, for example:

The graph shows a comparison between male and female employment rates by age groups.
There is a lower percentage of females in employment compared to males in all age groups except one! Which one?
The graph shows male employment rates rising up to age 35-44 and then falling.
The graph shows female employment rates rising up to age 20-24, then falling, then rising, then falling! Why is this pattern different to that for males?

However, when category labels in the graph are long it is better to display information using a horizontal bar graph.

HORIZONTAL BAR GRAPH

There are two advantages of a horizontal bar graph over a column graph:

category labels in a horizontal bar graph can be fully displayed (try fitting Advanced clerical and service persons neatly at the foot of a column!), and
it is easier to read the scale of a horizontal bar graph.

EMPLOYED PERSONS BY OCCUPATION AND SEX,AUSTRALIA, 1996 CENSUS

Graph: employed persons by occupation and sex during 1996 Census

('000)

Again, a careful look at the horizontal bar graph will allow you to draw several conclusions:

The graph compares employed males and females in occupation groups.
In four of the nine occupation groups more females are employed than males. Which are they?
One of the occupation groups has a very large difference (nearly 780,000) in the numbers of males and females employed within it. Which is it?

DOT CHART

The dot chart has been adopted by the ABS as the standard type of graph to display information. It is able to convey quite a lot of information in a simple way without clutter. It contrasts values very clearly, and can display many data values.

Graph: languages other then english spoken at home, Australia, 1996 Census

The simplicity of the above dot chart allows you to conclude that:

Italian was the most commonly spoken non-English language in Australian homes: 2.2% of the Australian population aged over 5 speak it at home.
Italian was followed by Chinese languages, Greek, Arabic, etc.

AGE PYRAMID

These are specially designed to represent the age structure of a population. They are a very effective way of showing change in a country’s age structure over time, or for comparing different countries.

The values of age groups may by expressed as numbers or percentages. If you are comparing the age distribution of different populations, it is better to use percentage than number values.

Image: Pyramid graphs - Age, by sex, Australia, 1991 and Age, by sex, Japan, 1991

Carefully study both age pyramids opposite and you should be able to see:

the male and female age groups with the largest number of people.

For Australia:

the age group with the largest number of people is the same for males and females; which is it?

For Japan:

the age group with the largest number of people is also the same for males and females; which is it?

(Note: the age group with the largest number of people is the same as the age group with the largest percentage of people.)

Why do you think:

the answers to the above two questions are different?

the shape of the age pyramid for Japan is different to that for Australia?

PICTOGRAPH

A pictograph is a graphic illustration of statistical information. Pictographs should be used carefully as they can, either accidentally or deliberately, misrepresent the message the graph is meant to convey.

A rule mentioned at the beginning of the section was that a graph should be accurate in a visual sense. Pictographs, if not drawn carefully, can be quite inaccurate.

PURCHASING POWER OF THE AMERICAN DOLLAR

The pictograph above shows how one American dollar in 1958 had shrunk to a value of 44 cents in 1978 (due to the effects of rising prices or inflation). If you think carefully, this means that one American dollar in 1978 could buy just under half as much as it could in 1958! So is there any problem with the depiction of statistics in the pictograph?

The size or area (length by breadth) of the dollars shown are in fact misleading. They should reflect the statistics or actual purchasing power of the dollar in the year in question. As 44 cents is just under half of one dollar, so the 1978 dollar area should be just under one half of the 1958 dollar area. This means that the 1978 dollar should be about twice as big as it is.

You may argue that this problem goes unnoticed by people when they look at a pictograph like this one, so it is not particularly important. However, the fact is that subconsciously many people interpret the dollar to have lost far more of its value than is the case.

It is also worth noting that the pictograph appeared during an American presidential election campaign in a leading newspaper, and would have been looked at by many voters!

PIE CHART

Pie charts are one of the most commonly used graphs. They have one advantage in that they are simple. However, one disadvantage is that it can be very difficult to see the difference in slice sizes when their values are similar. This is why it is important to label the slices with actual values, as in the example below.

Graph: Marital status of Australia's Population, 1996 Census

A pie chart is constructed by converting the percentage share of each category into the same percentage of 360 degrees. In the previous chart, for example:

the married category is 53.2%,
53.2% of 360°is 191.52°, and
using the radius in the 12 o’clock position as the origin, the angle of 191.52°(rounded to 192°) is measured with a protractor and a radius marked off .

This procedure is followed with remaining categories until the pie is complete. The final category need not be measured as its radius is already in position.

An important rule when drawing a pie chart is that segments are ordered by size (largest to smallest) in a clockwise direction.

It is best that segments number no more than five, so the chart does not become too cluttered.

The simplicity of the pie chart opposite tells you quickly that:

the majority of Australia’s population aged 15 and over were married at the time of the 1996 Census; and
just under a third were never married.

Note that if the Widowed and Divorced segments were not labelled with percentage values it would be difficult to tell quickly which segment was bigger.

NOTE:
Many computer packages will draw pie charts for you quickly and easily. However, research has shown that many people can make mistakes when trying to compare pie chart values. In general, bar charts get the same type of information across to people with less possibility for misunderstanding.

LINE GRAPH

A line graph is a very common way of presenting statistics. It is particularly useful when you want to display information over a time period. It should always be used when you want to show a trend in data over time.

Graph: Industrial disputes, Australia, 1971-96

The line chart above shows one obvious trend:

the number of working days lost through industrial disputes in Australia was far greater in the 1970s than during the 1980s and 1990s.

Can you tell from the graph:

the year in which the most working days were lost?

It is important when drawing a line graph that you use the correct scale. Otherwise the line’s shape can give an incorrect impression about information. Consider the following example:

Graph: male unemployment rates, Australia, 1978-84 - scale of 0-100

Graph: male unemployment rates, Australia, 1978-84 - scale of 0-10

Using a scale of 0 to 100 (top chart) does not effectively show the doubling of male unemployment rates between 1982 and 1983. However, choosing a scale of 0 to 10 (bottom chart) brings out this important message in the statistics.

HISTOGRAM

A histogram has a similar appearance to a column graph but no gaps between the columns. It is used to depict data from the measurement of a continuous variable.
Technically, the difference between column graphs and histograms is that:

in a histogram: frequency is measured by the area of the column, and

in a column graph: frequency is measured by the height of the column.

Graph: column graph showing distribution of vehicle speeds on a freeway

Generally, a histogram will have equal width bars, although when class intervals vary in size this will not be the case.

Choosing the appropriate width of the bars for a histogram is very important.

FREQUENCY POLYGON

A frequency polygon is a graph formed by joining the mid-points of histogram column tops. Obviously, they are only used when depicting data from the continuous variable shown on a histogram.

A frequency polygon smoothes out abrupt changes that may appear in a histogram, and is therefore useful for demonstrating continuity of the variable being studied.

Graph: Frequency Polygon showing distribution of vehicle speeds on a freeway

.
SUMMARY

Column graph: used when comparing data values is important, and there are five or fewer categories. When there are more than five, a dot chart should be used. Column graphs generally display data better than horizontal bar graphs, and are preferred where possible.
Horizontal bar graph: used when category names are too long to fit at the foot of a column. As with the column chart, it is more suited to five or fewer categories. When there are more than five categories, use a dot chart.
Dot chart: used when displaying a comparatively large number of categories and category order is unimportant. It is best used when portraying category values in descending order of size.
Age pyramid: used when representing population age structure.
Pictograph: only used by professional graphic artists, although simple pictorial presentations can be done by students. Care should be taken that comparisons are accurately depicted.
Pie chart: used for simple comparison of a small number of categories. Values should be markedly different, or differences may not be easily seen. Labelling sectors with their actual values overcomes this problem. In some cases, where data values are close to each other, a pie chart’s message may be easily misunderstood. A column or horizontal bar chart may be more useful.
Line graph: used for depicting data over time.
Histogram: this should be used with the same advice for a column graph, when depicting continuous variable data.
Frequency polygon: this should be used when depicting continuous variable data, and you want to smooth out abrupt changes that may appear in a histogram.

EXERCISES

1.	Over a period, say one week, keep a record of graphically presented statistics in a leading newspaper. Are the graph examples appropriate, or could any of the statistics have been presented better with a different type of graph?
2.	What type of graph would you choose to present the following information, and why would it be preferable over other types?
	a) Number of female students in each year level in your school. b) Annual road toll (number of fatalities in road traffic accidents) in your State for the last 30 years. c) Speed of the world’s fastest 20 animals. d) Population of China (including males and females).
4.	When would it be preferable to use a horizontal bar graph rather than a vertical bar graph?
5.	Obtain an official copy of the latest music charts for Australia. Produce graphs showing the different information they contain. For example, the number of weeks a record has been in the charts, or the ranking of the ‘Top Ten’.